The so-called master-slave system originated from a mechanical master-slave system in which a master robot and a slave robot are mechanically linked so as to work in coordination with each other. The mechanical master-slave system is advantageous in that the operator can have a direct feel of operation, but also disadvantageous in that: the degree of freedom in mechanism design is limited because of geometric restrictions between the operator and the master robot and also between the operator and the slave robot; the system naturally feels heavy to manipulate because the system is driven by human power; and further, the system has trouble in ensuring safety when abnormalities arise.
Therefore, although the mechanical master-slave system is still considered useful, the current mainstream is an electrical master-slave system in which the master robot and the slave robot are electrically interconnected but mechanically separated, and are operable independently of each other. In general, the electrical system can be flexibly controlled with electrical means or by means of software, and can have a mechanism that can be designed with flexibility, and further, the safety of the system can be ensured readily by constructing the system such that the operator is not involved in the working space of a high power actuator.
The electrical master-slave system having these characteristics has been developed mainly for such an application as remote control (i.e., teleoperation), and therefore, the study thereof was carried out mainly focusing on improvements in position and force repeatability, transparency, or communication time delay. An overview description will be provided below regarding basic types of bilateral control for the electrical master-slave system.
First, for convenience of explanation, the equations of motion that represents the dynamics of the master robot and the slave robot are defined by way of example as follows:[Expression 1]JmTfm+τm=Mm{umlaut over (q)}m+rm  (1);[Expression 2]τs=Ms{umlaut over (q)}s+rs+JsTfs  (2),where fm(t) is a master operating force applied to the master robot by the operator at time t, and fs(t) is a slave working force applied to the environment (i.e., a work object) by the slave robot at the same time t. Furthermore, respectively for the master robot and the slave robot, qm(t) and qs(t) are joint displacements, τm(t) and τs(t) are joint driving forces, Mm(qm) and Ms(qs) are inertia matrices, and rm(q•m, qm) and rs(q•s, qs) remainder terms aggregating effects other than inertia. Jm(qm) and Js(qs) are Jacobian matrices representing differential kinematics and satisfying the following relationship:[Expression 3]{dot over (x)}m=Jm{dot over (q)}m  (3);[Expression 4]{dot over (x)}s=Js{dot over (q)}s  (4),where xm(t) and xs(t) are displacements of an operating end of the master robot and a working end of the slave robot in a work coordinate system respectively corresponding to qm(t) and qs(t). Note that symbols, such as “(t)”, which indicate independent variables of a function might be omitted herein.
[Position-Symmetric Bilateral Control]
Position-symmetric bilateral control is bilateral displacement error servo control between the master and the slave. This control eliminates the need for a force sensor, and therefore, renders it possible to readily configure a relatively stable system. In the case where proportional control in the work coordinate system is used, control laws for the master robot and the slave robot are, for example, as shown below:[Expression 5]τm=JmTSf−1Kp(xa−Sp−1xm)  (5);[Expression 6]τs=JsTKp(Sp−1xm−xs)  (6),where Kp is a position control gain. Moreover, Sf is the scale ratio of force from the master robot to the slave robot, and Sp is the scale ratio of displacement from the slave robot to the master robot.
From the master dynamics (1), the slave dynamics (2), the master control law (5), and the slave control law (6), the following expression is obtained.[Expression 7]fm=Jm−T(Mm{umlaut over (q)}m+rm)+Sf−TJs−T(Ms{umlaut over (q)}s+rs)+Sf−1fs  (7)In this manner, in the position-symmetric bilateral control, the influence of the master dynamics is added to the master operating force fm as is, and the influence of the slave dynamics and the slave working force fs are also added by a factor of Sf−1.
[Force-Reflecting Bilateral Control]
In force-reflecting bilateral control, a working force sensor for measuring the slave working force fs is disposed at the working end of the slave robot in order to “reflect” the slave working force fs in the force of driving the master. In this case, the master control law is as shown below. Note that the slave control law is the same as Expression (6) for the position-symmetric bilateral control.[Expression 8]τm=−JmTSf−1fs  (8)
From the master dynamics (1) and the master control law (8), the following expression is obtained.[Expression 9]fm=Jm−T(Mm{umlaut over (q)}m+rm)+Sf−1fs  (9)In the case of the force-reflecting bilateral control, as in the case of the position-symmetric bilateral control, the influence of the master dynamics is added to the master operating force fm as is, and the slave working force fs is also added by a factor of Sf−1. On the other hand, the master operating force fm is not influenced by the slave dynamics.
[Force-Reflecting Servo Bilateral Control]
In force-reflecting servo bilateral control, an operating force sensor for measuring the master operating force fm is disposed at the operating end of the master robot, a working force sensor for measuring the slave working force fs is disposed at the working end of the slave robot, and a force error servomechanism is configured on the master side. In this case, the master control law is as shown below.[Expression 10]τm=JmTKf(fm−Sf−1fs)−JmTSf−1fs  (10)The above expression includes force error servo control in addition to the master control law (8) for the force-reflecting type. Note that Kf is a force control gain. Moreover, the slave control law is the same as in Expression (6) for the position-symmetric bilateral control.
From the master dynamics (1) and the master control law (10), the following expression is obtained. Note that I is an identity matrix.[Expression 11]fm=(I+Kj)−1Jm−T(Mm{umlaut over (q)}m+rm)+Sf−1fs  (11)
By increasing the force control gain Kf in the above expression to a sufficient degree, the following expression can be obtained.[Expression 12]fm≃Sf−1fs  (12)In this manner, in the case of the force-reflecting servo bilateral control, by sufficiently increasing the force control gain Kf, the influence of the master dynamics on the master operating force fm can be reduced to a negligible degree, so that only the slave working force fs is added to the master operating force fm by a factor of Sf−1. However, for implementation reasons, the stability of bilateral control decreases as the force control gain Kf increases, and therefore, it is difficult to eliminate the influence of the master dynamics on the master operating force fm, so that complete transparency cannot be achieved.
[Parallel Bilateral Control]
In Non-Patent Document 1, Miyazaki et al. propose parallel bilateral control, which is an improvement to the traditional serial connection method for bilateral control. In the case of the parallel type, an operating force sensor for measuring the master operating force fm is disposed at the operating end of the master robot, a working force sensor for measuring the slave working force fs(t) is disposed at the working end of the slave robot, and a parallel displacement error servo mechanism is configured by the master and the slave. In this case, the control laws are as shown below:[Expression 13]τm=JmTKp(xd−Sp−1xm)  (13);[Expression 14]τs=JsTSjKp(xd−xs)  (14);[Expression 15]xd=Kf(fm−Sf−1fs)  (15),Note that xd(t) is a target displacement for each of the operating end of the master robot and the working end of the slave robot at time t in the work coordinate system.
From the master dynamics (1), the slave dynamics (2), the master control law (13), the slave control law (14), and the target displacement calculation (15), the following expression can be obtained.[Expression 16]fm=(I+2KpKf)−1Jm−T(Mm{dot over (q)}m+rm)+(I+2KpKf)−1Sf−1Js−T(Ms{umlaut over (q)}s+rs)+(I+2KpKf)−1*Kp(Sp−1xm+xs)+Sf−1fs  (16)Furthermore, by increasing the force control gain Kf in the above expression to a sufficient degree, the following expression can be obtained.[Expression 17]fm≃Sf−1fs  (17)The advantage of the parallel bilateral control is that phase lag is reduced by providing the master control law and the slave control law in parallel, resulting in bilateral control with increased stability. However, in the case of the parallel bilateral control, the master operating force fm is influenced by both the master dynamics and the slave dynamics, as can be seen from the first and second terms of the right-hand side of Expression (16). Moreover, in the case of the parallel bilateral control, even a spring constant term, which is not included in the original dynamics, is added to the master operating force fm, as can be seen from the third term of the right-hand side of Expression (16). Such influences can be reduced to a negligible degree by increasing the force control gain Kf, but for implementation reasons, even the increased stability of the bilateral control can be weakened as the force control gain Kf increases, and therefore, even the parallel bilateral control cannot achieve complete transparency.
[Force-Projecting Bilateral Control]
The basic types of bilateral control, including the position-symmetric type, the force-reflecting type, the force-reflecting servo type, and the parallel type, have been described so far, and conventional bilateral control, including these types, has Problems 1 through 6 as follows:
[Problem 1]A problem common among the force-reflecting type, the force-reflecting servo type, and the parallel type.
Information about the slave working force fs is required for control, and therefore, application to a system in which the working force sensor cannot be mounted on the slave robot is not possible.
[Problem 2]A problem common between the position-symmetric type and the force-reflecting type.
Control drives the system in accordance with displacement error of the master robot, and therefore, it is necessary to set the inertia and the friction of the master robot as little as possible, such that displacement error of the master robot can be readily generated by human power, i.e., high backdrivability is ensured, resulting in difficulty in achieving a highly accurate mechanism.
[Problem 3]A problem common between the force-reflecting servo type and the parallel type.
Control is intended to achieve transparency, and therefore, the operator mainly senses only the dynamics of the environment (i.e., a work object).
[Problem 4]A problem common among the position-symmetric type, the force-reflecting type, the force-reflecting servo type, and the parallel type.
The slave robot is always connected to the master robot, and therefore, there is a risk that unstable behavior might be excited in the system solely by an external force applied to the slave robot, even without the operator manipulating the master robot.
[Problem 5]A problem common among the position-symmetric type, the force-reflecting type, the force-reflecting servo type, and the parallel type.
A command value for the slave robot is position-related, and the slave dynamics need to be cancelled by positional control, which imposes a large burden on the control system. In addition, the control law based on the positional control does not necessarily allow another control law to be superimposed thereon.
[Problem 6]A problem common among the position-symmetric type, the force-reflecting type, the force-reflecting servo type, and the parallel type.
When positional control in the work coordinate system is applied to the slave robot, a singular configuration problem might arise, so that control failure might occur when the posture of the slave robot approaches a singular configuration.
As new bilateral control capable of neatly solving these problems, the present inventor proposes the basic configuration of “force-projecting bilateral control” in Patent Document 1. In the force-projecting type, an operating force sensor for measuring the master operating force fm is disposed at the operating end of the master robot, and the measured master operating force fm is “projected” to the force of driving the slave robot. In the force-projecting bilateral control, the master control law and the slave control law are, for example, as shown below:[Expression 18]τm=JmTKp(Spxs−xm)  (18)[Expression 19]τs=JsTSffm  (19)
From the slave dynamics (2) and the slave control law (19), the following expression can be obtained.[Expression 20]fm=Sf−1JsT(Ms{umlaut over (q)}s+rs)+Sf−1fs  (20)In this manner, in the case of the force-projecting bilateral control, the influence of the slave dynamics and the slave working force fs are added to the master operating force fm by a factor of Sf−1. That is, the force-projecting bilateral control is an approach to measure the master operating force fm applied to the master robot by the operator, rather than the slave working force fs applied to the environment (i.e., a work object) by the slave robot, and allow the master to pass force information forward to the slave while allowing the slave to feed displacement information back to the master.
The force-projecting bilateral control has Characteristics 1 through 6 as shown below:
[Characteristic 1] Applicable to even a system in which the working force sensor cannot be mounted on the slave robot, because no information about the slave working force fs is needed.
[Characteristic 2] Not requiring the master robot to have backdrivability because the system is driven by the master operating force fm applied to the master robot by the operator, rather than in accordance with displacement error of the master robot, so that the master robot can be rendered to be a mechanism which is robust enough to withstand human power and highly accurate.
[Characteristic 3] Being control that is intended to achieve “projectivity” to be described later, rather than transparency, and therefore, allowing the operator to feel the dynamics of the environment (i.e., a work object) and even the slave dynamics, but no master dynamics.
[Characteristic 4] No risk of unstable behavior being excited in the system solely by an external force applied to the slave robot because the connection from the master robot to the slave robot is shut off (i.e., the connection therebetween changes from bilateral to unilateral) unless the operator applies the master operating force fm to the master robot.
[Characteristic 5] The command value for the slave robot is related to drive power (force and torque), rather than position-related, which facilitates the implementation of the slave control law, and imposes little burden on the control system. The control is based on drive power, and therefore, any type of control based on drive power can be superimposed on the slave control law.
[Characteristic 6] The slave robot is not position-controlled but is controlled in terms of drive power, and therefore, no singular configuration problem occurs even if the control in the work coordinate system is applied, so that control failure does not occur even if the posture of the slave robot approaches a singular configuration.
Characteristics 1 through 6 above will be described in more detail.
First, “Characteristic 1” will be described. In most of the conventional types of bilateral control, such as the force-reflecting type, the force-reflecting servo type, and the parallel type, the working force sensor for measuring the slave working force fs is mounted on the working end of the slave robot in order to enhance the feel of operation of the master-slave system. However, some systems often involve difficulty in mounting the working force sensor on the working end of the slave robot.
For example, in the case of a power-amplifying master-slave system, the slave robot has a high power actuator disposed thereon. Accordingly, the slave robot is required to be hardware that can withstand such high power. However, multi-axis force sensors, which are generally used as working force sensors, are delicate and expensive, and therefore, it is difficult to mount such a sensor on the working end of the high-power slave robot. Moreover, in the case of a master-slave system serving as a surgical robotic system, the slave robot is required to be invasive to the human body, and the hardware thereof needs to be subjected to high-level cleaning, disinfection, and sterilization (autoclave sterilization). It is difficult to mount a multi-axis force sensor, which is a complex electronic device, on the working end of such a slave robot.
In the case of the force-projecting bilateral control, it is simply required to mount a force sensor (i.e., an operating force sensor) on the master robot, which does not have such mounting difficulty. In addition, the slave robot can be provided in the simplest configuration only including an actuator and a displacement sensor. Thus, it is relatively easy to equip most systems with the force-projecting bilateral control.
Next, “Characteristic 2” will be described. In most of the conventional types of bilateral control, such as the position-symmetric type and the force-reflecting bilateral control, the system is driven not directly by the master operating force fm applied to the master robot but in accordance with displacement error of the master robot caused by the master operating force fm. In this case, to enhance the feel of operation, the master robot is required to be so-called backdrivable so as to be movable even by human power. Moreover, to this end, it is necessary to reduce the inertial mass and the friction of the master robot as much as possible. Under such circumstances, in the case of the conventional bilateral control, the master robot is naturally a powerless and delicate mechanism with a low reduction ratio. This means that the master robot tends to lack the rigidity and output power required to provide a reaction force to the operator with high accuracy.
On the other hand, in the case of the force-projecting bilateral control, the system is driven by the master operating force fm applied to the master robot, and therefore, the master robot does not have to be backdrivable so long as the master operating force fm can be measured. Accordingly, in the case of the force-projecting bilateral control, the master robot can be provided as a robust and powerful mechanism with a high reduction ratio, and also can provide a reaction force to the operator with high accuracy. Note that since the mechanism is intended for the master robot, it is simply required to ensure that the mechanism is robust enough to merely withstand human power. Accordingly, being provided with the operating force sensor for measuring the master operating force fm is not a disadvantage when ensuring robustness, even if the operating force sensor is a multi-axis force sensor.
Next, “Characteristic 3” will be described. In the case of both the force-reflecting type and the force-reflecting servo bilateral control where the working force sensor is disposed on the slave robot, particularly where the working force sensor is provided on the working end of the slave robot, the operator does not feel the slave dynamics, as can be appreciated from Expressions (9) and (11). On the other hand, the operator feels the master dynamics, and therefore, the critical norm “transparency” for the conventional bilateral control is realized by reducing the influence of the master dynamics to a negligible degree. That is, in the case of the conventional bilateral control, also for a different reason from that described in conjunction with “Characteristic 2”, the master robot needs to be a powerless and delicate mechanism with a low reduction ratio.
However, the present inventor submits that there is room for reconsideration of the very norm “transparency” for the conventional master-slave systems, and therefore, proposes herein a new norm. More specifically, as opposed to the conventional norm “transparency” intended to render both the master dynamics and the slave dynamics “transparent” and provide the operator with a direct feel of operation of only manipulating the environment (i.e., a work object), the new norm is intended to “project” the master operating force fm from the operator as the force of driving the slave and also “project” the slave dynamics, even including the dynamics of the environment (i.e., a work object), as a master displacement, thereby providing the operator with the feel of operation of manipulating the environment (i.e., a work object) and even the slave robot. This new norm is referred to below as “projectivity”. It can be said that the more accurate the projection of the master operating force fm to the force of driving the slave becomes, or as the more accurate the projection of the dynamics of the environment (i.e., a work object) and the dynamics of the slave to a master displacement becomes, the higher the degree of projectivity becomes.
To put it qualitatively, in the case of a conventional master-slave system with high transparency, the operator does not feel the sense of the master-slave system, and therefore, feels as if he/she was directly manipulating the environment (i.e., a work object) using his/her own body. On the other hand, in the case of a master-slave system with high projectivity, the operator does not feel the sense of the master robot, and therefore, feels as if he/she was moving the slave robot using his/her own body and manipulating the environment (i.e., a work object) through the slave robot. That is, in other words, it can be said that the norm “transparency” aims to realize “the sense of manipulating a target with an actual human body”, whereas the norm “projectivity” aims to realize “the sense of manipulating a target via an exoskeleton”.
Therefore, the present inventor refers to the state where ideal projectivity is realized as “exoprojection”. By realizing exoprojection, it is rendered possible to allow the operator to feel as if the slave robot, whose portions at least other than the trunk operate mechanically independent of the master robot, is mechanically interlocked with the master robot even at the portions other than the trunk. Moreover, it is also rendered possible for the operator not to feel the sense of the master robot, which merely serves as an operating device, but to feel the slave robot, which serves as a working device, to be an exoskeleton actually being put on the operator himself/herself. The term “exoprojection” derives from such an effect.
In Non-Patent Document 2, on p. 575, Yokokohji et al. define “ideal response(s)”, which is synonymous with the term “transparency”, as follows:
“when the operator applies a certain operating force, positional responses xm and xs of master and slave arms always match force responses fm and fs regardless of the target to be handled”.
In accordance with the notation considering the scale ratio (Sf, Sp) herein, the ideal responses can be represented as shown below.[Expression 21]xm=Spxs  (21)[Expression 22]Sffm=fs  (22)
In Non-Patent Document 2, the state where the ideal responses are realized is referred to as the state where object teleperception is possible. However, to realize such ideal responses, all dynamics of the master-slave system, along with inertia, need to be eliminated, which imposes a large burden on the control system, resulting in a high probability of unstable bilateral control (see Non-Patent Document 3). This can also be appreciated from the fact that the force control gain Kf→∞ is essential to realize the force transparency (22) in Expression (11) for the force-reflecting servo bilateral control or in Expression (16) for the parallel bilateral control.
On the other hand, ideal responses for the“projectivity” defined by the present inventor can be represented as shown below.[Expression 23]xm=Spxs  (23)[Expression 24]JsTSffm=τs  (24)
The state where the ideal responses are realized is “exoprojection”. To realize exoprojection, it is not necessary to eliminate the slave dynamics. This is advantageous particularly for the power-amplifying master-slave system. In the power-amplifying master-slave system, the slave robot is often larger than the master robot, and is also dominant in terms of inertia. Reducing the burden of eliminating the dominant inertia of the slave robot contributes considerably to enhancement of stability of the control system.
Furthermore, as a norm, projectivity is more advantageous than transparency particularly in the case where the operator acquires the skills of “machine-friendly manipulation” in the master-slave system (with differences in structure, degree of freedom, and scale) in which the master robot and the slave robot have considerably different dynamics from each other.
For example, in the case of a master-slave system with a difference in scale where the master robot and the slave robot are significantly different in scale, by using projectivity as a norm, it is rendered possible to present the operator with scale effects not only of the environment (i.e., a work object) but also of the slave dynamics. The operator can be prompted to perform appropriate manipulation by being presented with the effect of inertia caused in the case where the slave robot is larger than the master robot (more specifically, in such a state where the master robot is moved around by the slave robot keeping on moving inertially), so that it can be expected that the operator makes manipulation efficient and optimal using his/her own skill. In the case of a system making “transparency”, rather than “projectivity”, as a norm, the operator is not presented with the scale effect of the slave dynamics, and therefore, it is not expected that the operator performs such efficient and optimal manipulation.
As described above, in the case of the force-projecting bilateral control, by disposing the operating force sensor at the operating end of the master robot, it is rendered possible to make the master dynamics transparent, as is indicated by Expression (20), and achieve high projectivity, i.e., exoprojection, to allow the operator to be provided with the sense of manipulating the environment (i.e., a work object) through the slave robot. In addition, in the case of the force-projecting bilateral control, to realize the force-related projectivity expressed by Expression (24), it is not necessary to make the force control gain Kf infinite.
Next, “Characteristic 4” will be described. In the case of the master operating force fm=0 where the operator does not act on the master robot, the master-slave system is driven solely by an external force −fs. The external force −fs can be obtained for the position-symmetric type by Expression (7), also for the force-reflecting type by Expression (9), and further for the force-reflecting servo type by Expression (11), as shown below.[Expression 25]−fs=SjJmT(Mm{umlaut over (q)}m+m)+Js−T(Ms{umlaut over (q)}s+rs)  (25)[Expression 26]−f=SfJm−T(Mm{umlaut over (q)}m+rm)  (26)[Expression 27]−fs=Sf(I+Kf)−1Jm−T(Mm{umlaut over (q)}m+rm)  (27)
Expressions (25) through (27) indicate that in the case of the conventional bilateral control (such as the position-symmetric type, the force-reflecting type, and the force-reflecting servo type), when the slave robot receives the external force −fs, the slave robot operates under the influence of the dynamics of the master robot, which is merely an operating device. Moreover, depending on the situation, there is a risk of unstable behavior being excited in the master-slave system solely by the external force −fs applied to the slave robot. Although not described herein, the same can be said of the parallel bilateral control. Regarding this problem, Non-Patent Document 4 points out on p. 24 that in the case of both the force-reflecting type and the force-reflecting servo bilateral control, when the operator takes his/her hand off the operating end of the master robot, the system tends to exhibit unstable behavior. The tendency becomes more marked particularly in the case where the force control gain Kf is set high so as to increase transparency both in the force-reflecting servo type and the parallel bilateral control.
On the other hand, in the case of the force-projecting bilateral control, the external force −fs can be obtained by the following expression based on Expression (20).[Expression 28]−fs=Js−T(Ms{umlaut over (q)}s+rs)  (28)The slave robot operates under the influence of its own dynamics upon reception of the external force −fs. Moreover, the external force −fs is not influenced by the master dynamics at all, and therefore, it can be appreciated that, where the master operating force fm=0, the connection from the master to the slave is automatically shut off, resulting in unilateral connection regardless of the force control gain Kf. In this manner, in the case of the force-projecting bilateral control, there is no risk of unstable behavior being excited in the master-slave system solely by the external force −fs applied to the slave robot.
Next, “Characteristic 5” will be described. In the master-slave systems, the master robots are provided only to be operated by humans, and therefore, the master robots are sized to such a scale as to be readily operable by humans, and are placed in environments comfortable to humans. However, the slave robots are required to employ a number of hardware structures so as to be operable in a wide variety of environments in accordance with tasks to be achieved. For example, the power-amplifying master-slave system requires the slave robot to output high power, and therefore, the slave robot might employ a hydraulic actuator, rather than an electromagnetic actuator. Also, in a master-slave system serving as a surgical robotic system, the slave robot might employ a pneumatic actuator. Furthermore, in most of the conventional types of bilateral control, the operator's will is reflected in specifying a target position of the slave robot, so that the slave robot is position-controlled.
As is well-known, when compared to the electromagnetic actuator, the hydraulic actuator and the pneumatic actuator have low position (trajectory) control performance. Accordingly, to accurately reflect the operator's will in the hydraulic or pneumatic actuator using the conventional bilateral control, it is necessary to apply a high-level and complicated positional control law, and implementing such a control law is expected to be difficult.
However, in the case of the force-projecting bilateral control, the operator's will is reflected in specifying a target driving force for the slave robot, and the slave robot is controlled in terms of driving force. In the case of force-projecting bilateral control employing a hydraulic or pneumatic actuator, the slave robot is controlled in terms of driving force by specifying a target pressure, rather than a target position, of the hydraulic or pneumatic actuator. Such pressure control of a hydraulic or pneumatic actuator is generally performed using a hydraulic or pneumatic control valve, and can be implemented without difficulty.
It is a matter of course that even if the force-projecting bilateral control is implemented so as to perform driving force control, the operator is not ensured to perform positional control on the slave robot with high accuracy, and it can be said that performing high-level and complex positional control, as is performed by a computer in accordance with the control law for the conventional bilateral control, is left to the operator's skill. However, it is without doubt that driving force control is implemented with ease, and the operator's will is accurately reflected in the slave robot as slave driving force. In addition, in the case of the force-projecting bilateral control, the operator can even intuitively know whether controllability of the hydraulic or pneumatic actuator is good, which is rendered less noticeable by the positional control law in the conventional bilateral control.
Furthermore, although the driving force control is left to the operator's skill, if there is any nonlinearity in slave dynamics which cannot be handled by the operator, the operator's skill can be backed up by superimposing dynamics compensation algorithms (e.g., gravity compensation and friction compensation) on the driving force control for the slave robot. In the case of the force-projecting bilateral control where the slave robot is controlled in terms of driving force, it is possible to simply superimpose control laws on each other, and vast knowledge on driving force control accumulated over a long history of robot control engineering can be utilized for backing up the operator's skill. For example, in one application, it is possible that the operator is allowed to feel the inertia of the slave robot, which is useful in manipulation, whereas nonlinear terms for the slave robot, which make manipulation difficult, are eliminated through compensation. Alternatively, it is also possible that different types of low-gain trajectory control for the slave robot are superimposed as if the operator was taken by the hand over the exoskeleton and guided, or a virtual wall to limit the range of movement of the slave robot is superimposed on the control for the slave robot. In the case where the slave robot is position-controlled, it is not necessarily possible to simply superimpose such control laws on each other, as described earlier.
Next, “Characteristic 6” will be described. In the master-slave system, the master robot is required to have operability, and the slave robot is required to have workability. To improve operability, the master robot needs to be designed ergonomically, whereas to improve workability, the slave robot needs to be designed so as to be adapted to tasks to be achieved. Accordingly, the master robot and the slave robot are naturally different in structure. Such a master-slave system including a master robot and a slave robot which are different in structure will be referred to as a double-structure master-slave system.
In the case of a single-structure master-slave system, there are limitations to enhancing both operability and workability. Accordingly, high-level master-slave systems inevitably become of a double-structure type. Moreover, it is typical of such a double-structure master-slave system to perform control in the work coordinate system, and also in the study up to this point herein, the control laws are premised by the control being performed in the work coordinate system.
In general, when a robot is position-controlled in the work coordinate system, the singular configuration problem occurs. The singular configuration refers to the posture of the robot (singular posture) for which the Jacobian matrix is irregular (i.e., no inverse matrix is obtained). At the singular configuration, the direction of the movement of the robot in the work coordinate system is limited. In the case where the robot's target trajectory is determined in the work coordinate system, the joint velocity for realizing the target trajectory becomes excessively high in the vicinity of the singular configuration. In addition, the actual robot can only have a limited joint velocity, so that there is a possibility where positional control in the work coordinate system might fail in the vicinity of the singular configuration. This encapsulates the singular configuration problem. Even if the position control law does not involve the inverse of the Jacobian matrix in computation, as in the case of Expression (6), positional control failure also occurs in the vicinity of the singular configuration. This is physical failure accompanied by coordinate transformation. Accordingly, such positional control failure cannot be prevented by computational contrivance.
In the conventional master-slave systems, the slave robot is position-controlled, but if the positional control is performed in the work coordinate system, the singular configuration problem occurs. More specifically, positional control failure occurs in the vicinity of the singular configuration unless approach to the vicinity of the singular configuration is avoided. On the other hand, if the slave robot is caused to move so as to avoid the vicinity of the singular configuration in order not to risk failure, additional disadvantages which are difficult to overcome arise as follows:
i) the working space of the slave robot is narrowed, leading to the need to increase the scale of the robot more than necessary; and
ii) the singular configuration for the slave robot cannot be positively utilized for task achievement.
Note that Non-Patent Document 5 describes in detail an approach to positively utilize the singular configuration.
As a countermeasure against the singular configuration problem, Non-Patent Document 6 describes on p. 476 a method in which, when any joint of the master robot or the slave robot reaches the limit of the range of movement or a singular configuration, feedback to the master is made in order to cause an opposite force to be exerted. Moreover, to solve the singular configuration problem with the double-structure master-slave system, Non-Patent Document 7 proposes a method in which assist gain is adjusted in accordance with the distance from a singular configuration (manipulability measure). Both of these methods are a kind of approach to avoid the singular configuration by causing the feel of manipulation to be heavy in the vicinity of the singular configuration and thereby allowing the operator to know that the singular configuration is approaching. That is, even by using the approaches of Non-Patent Documents 6 and 7, it is still not possible to overcome the aforementioned disadvantages i) and ii).
As another countermeasure to the singular configuration problem, Non-Patent Document 8 proposes a singular configuration consistent approach. This approach is a control method utilizing the adjugate of the Jacobian matrix, and inhibits the joint velocity from becoming excessively high and thereby preventing positional control failure. In addition, it is rendered possible to eliminate the need to avoid the singular configuration and thereby overcome the disadvantages i) and ii). However, although no failure occurs, the joint velocity is still limited, and therefore, detriment to operability in the vicinity of the singular configuration is unavoidable. Non-Patent Document 8 has an approach devised to not cause detriment to operability, and the approach of Non-Patent Document 8 can suppress such detriment but cannot be used to cause no detriment at all.
On the other hand, in the case of the force-projecting bilateral control, the slave robot is not position-controlled, but is controlled in terms of driving force. For example, in the case where the driving force control is implemented on the slave robot, as in Expression (19), it is simply necessary to obtain the transpose JsT of the Jacobian matrix on the basis of differential kinematics, and the inverse Js−1 of the Jacobian matrix does not need to be obtained. In the case of the force-projecting bilateral control where the driving force control is performed on the slave robot, inherently, the slave robot does not have the singular configuration problem, therefore, it is not necessary to avoid the singular configuration for the slave robot, and there are no such disadvantages i) and ii) as mentioned above. In other words, the force-projecting bilateral control has the following advantages:
i′) the entire range of movement (i.e., the entire working space) of the slave robot can be utilized; and
ii′) the singular configuration for the slave robot can be positively utilized for task achievement.
Non-Patent Document 9 mentions on p. 116 a “position-force loop” as control in the opposite direction to the force-reflecting bilateral control and the force-reflecting servo bilateral control, but no other detailed description of such control is given in the document, and therefore, conceivably this control does not correspond to the force-projecting bilateral control.
Furthermore, Non-Patent Document 9 describes on p. 116 that “the position-force loop is not implemented effectively”, and also describes the reason as follows: “force control for the slave robot is unstable”. These descriptions suggest that the common technical knowledge in the art is that implementation of the “position-force loop” is extremely difficult or even impossible.